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President Donald Trump attends a roundtable discussion on border security with local leaders, Friday Jan. 11, 2019, in the Cabinet Room of the White House in Washington.

President Donald Trump avoided directly answering when asked whether he currently is or has ever worked for Russia after a published report said law enforcement officials, concerned about his behavior after he fired FBI Director James Comey in 2017, had begun investigating that possibility.

Trump responded to the story Saturday during a telephone interview broadcast on Fox News Channel after host Jeanine Pirro, a personal friend, asked the Russia question.

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"I think it's the most insulting thing I've ever been asked," Trump said. "I think it's the most insulting article I've ever had written, and if you read the article you'll see that they found absolutely nothing."

Trump never answered Pirro directly, but went on to assert that no president has taken a harder stance against Russia than he has.

"If you ask the folks in Russia, I've been tougher on Russia than anybody else, any other ... probably any other president, period, but certainly the last three or four presidents."

Trump's claim was disputed by Virginia Sen. Mark Warner, the top Democrat on the Senate Intelligence Committee. He said almost all the sanctions on Russia arose not in the White House but in Congress, due to concerns by members of both parties about Moscow's actions. Warner accused the White House of being very slow to put in place the penalties.

And while Republican lawmakers have reiterated the same claims that Trump has been tougher on Russia than his Democratic predecessor Barack Obama, Sen. Ted Cruz said Sunday that as a member of the Senate Judiciary Committee he would consider any evidence produced but did not know details about the probe.

"I know what was reported publicly in the media, and I sit on the Senate Judiciary Committee, so we will consider any allegations that come forward," Cruz told "Meet the Press" moderator Chuck Todd in response to a question about the Times report.

The Times reported that FBI agents and some top officials became suspicious of Trump's ties to Russia during the 2016 presidential campaign but didn't open an investigation at that time because they weren't sure how to approach such a sensitive probe.

Trump's behavior in the days around Comey's May 2017 firing helped trigger the counterintelligence part of the probe, according to the newspaper.

In the inquiry, counterintelligence investigators sought to evaluate whether Trump was a potential threat to national security. They also sought to determine whether Trump was deliberately working for Russia or had unintentionally been influenced by Moscow.

Trump tweeted early Saturday that the report showed that the FBI leadership "opened up an investigation on me, for no reason & with no proof" after he had fired Comey.

Robert Mueller took over the investigation when he was appointed special counsel soon after Comey's firing. The overall investigation is looking into Russian election interference and whether Trump's campaign coordinated with the Russians, as well as possible obstruction of justice by Trump. The Times says it's unclear whether Mueller is still pursuing the counterintelligence angle.

Sen. Chris Coons, D-Del., said the report "may well suggest what it was that helped start this investigation in the first place." He and other Democratic senators said this report and others within the past week questioning Trump's behavior toward Russia give new urgency to the need for the Mueller investigation to be allowed to run its course.

A new report in The Washington Post said Trump went to extraordinary lengths to conceal details of his conversations with Russian President Vladimir Putin even from high-ranking officials in his own administration. The report cited unnamed current and former U.S. officials.

In the Fox News interview, Trump questioned why the newspaper made such a "big deal" out of his discussions with Putin in Helsinki last summer. "Anybody could have listened to that meeting, that meeting is up for grabs."

Sen. Ron Johnson, R-Wis., defended the president, who he said was "burned earlier by leaks of other private conversations."

Trump's lawyer Rudy Giuliani told the Times he had no knowledge of the counterintelligence inquiry but said that since it was opened a year and a half ago and they hadn't heard anything, apparently "they found nothing."

Republican Sen. Lindsey Graham, who is close to Trump and chairs the Judiciary Committee, said he intends to ask the FBI director if there was a counterintelligence investigation into the president. "If this really did happen, Congress needs to know about it and what I want to do is make sure how could the FBI do that?"

Trump has repeatedly and vociferously denied collusion with the Russians.

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Also Sunday, Senate Democratic leader Chuck Schumer said he will force a vote in the coming days on the Treasury Department's decision to ease sanctions on three companies connected to Russian oligarch Oleg Deripaska.

Treasury Secretary Steven Mnuchin last week defended the decision, saying the companies are undergoing a major restructuring to "sever Deripaska's control and significantly diminish his ownership." He saids Deripaska himself and any companies he controls remain under sanctions.

Schumer, however, contends the Russian oligarch maintains significant influence on these companies, including the aluminum manufacturing giant Rusal, and said it's important the sanctions remain in place while Mueller's investigation proceeds. Deripaska has figured into the investigation due to his ties to former Trump campaign chairman Paul Manafort.